login
Decimal expansion of Sum_{k >= 1} floor(k*e^(Pi*sqrt(163/9)))/2^k.
0

%I #11 May 13 2024 14:06:14

%S 1,2,8,0,6,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,

%T 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,

%U 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9

%N Decimal expansion of Sum_{k >= 1} floor(k*e^(Pi*sqrt(163/9)))/2^k.

%H J. M. Borwein and P. B. Borwein, <a href="https://doi.org/10.2307/2324993">Strange Series and High Precision Fraud</a>, The American Mathematical Monthly, Vol. 99, No. 7 (1992), pp. 622-640.

%F Approximately 1280640, correct to at least half a billion digits: see Sum 10 in Borwein and Borwein (1992), p. 623.

%e 1280639.9999999999999999999999999999999999999999999999999999...

%t First[RealDigits[Sum[Floor[k*E^(Pi*Sqrt[163/9])]/2^k, {k, 400}], 10, 100]]

%Y Cf. A000796, A001113, A038152, A190575, A039661.

%K nonn

%O 7,2

%A _Paolo Xausa_, May 11 2024